MPPT Control for a PMSG-Based Grid-Tied Wind Generation System Xin Wang, Subbaraya Yuvarajan, Senior Member, IEEE, and Lingling Fan, Senior Member, IEEE Abstract—Permanent magnet synchronous generators (PMSGs) are commonly used as a variable speed generator in wind energy systems. This paper describes a maximum power point tracking (MPPT) scheme for a PMSG-based wind energy conversion system (WECS) in which a buck-boost converter is used to handle a wide range of wind speeds. A closed-loop with a PWM inverter forces the WECS to extract the maximum power available from the wind turbine by shifting the phase angle of output voltage at a given wind speed. The output power is fed to the grid. The mathematical model of the wind power system is built and simulated by MATALB/SIMULINK software. Simulation results show that the proposed control scheme has a good dynamic performance and operates the wind generation system with the maximum efficiency. Index Terms—maximum power point tracking, permanent magnet synchronous generator, phase shift, pulse width modulation, wind energy I. INTRODUCTION V ARIABLE-SPEED wind generation systems make it possible to extract the maximum energy from wind with widely varying speeds. The permanent magnet synchronous generators (PMSGs) are suitable for small variable-speed wind turbine generator systems. The wind generation system with a PMSG represents one important trend of development for wind power applications with numerous advantages like higher efficiency due to the absence of field copper loss, lower operating speed due to higher number of poles with smaller pole pitch, and the elimination of gearbox [1], [2]. Smaller wind turbines use fixed pitch angle without the need for additional pitch control. The power from the wind energy conversion system (WECS) is normally fed to an ac grid. Like in any wind power system, it is desirable to extract the maximum power available at a given wind speed. There are different methods used to extract the maximum power from the wind. Different control concepts for maximum power point tracking (MPPT) in WECS with PMSG are described and the performance for each is compared in [3]. The MPPT methods can be broadly classified as those which use sensors and those which do not use sensors. They are also classified based on the type of control, such as fuzzy logic based control [4] and sliding mode control [5]. Xin Wang and S. Yuvarajan are with the Department of Electrical and Computer Engineering, North Dakota State University, Fargo, ND 58108 USA (email: [email protected]; [email protected]). Lingling Fan is with the Department of Electrical Engineering, University of South Florida, Tampa, USA (email: [email protected]). To convert the variable-frequency output voltage from the PMSG into an ac voltage of the grid frequency (60Hz), two typical power converter topologies for small wind turbine systems with PMSG are presented and explained in [6]. The first configuration uses a diode-bridge rectifier, a boost converter and an inverter; and the second configuration uses a back-to-back converter system. The MPPT is implemented on the dc-dc converter in the former system and on the PWM inverter in the latter one. In the dc-dc converter, the duty cycle is controlled, and in the PWM inverter the modulation index is controlled, for MPPT. An input-output feedback linearization (IOL) technique is applied to design the high-performance nonlinear current controller on the PWM rectifier in [7]. A sensorless MPPT control strategy on the PWM inverter is implemented in [8], which is achieved without a wind speed sensor and mechanical sensors such as rotor speed sensor and position sensor. A new variable-speed WECS with a PMSG and Z-source inverter is proposed in [9]. Compared to the conventional WECS with boost converter, the number of semiconductor switches used in [9] is reduced by one and the system reliability is improved. Another nonlinear approach for MPPT is also presented in [10]. It uses a matrix converter and the controller is based on the nonlinear adaptive backstepping method which is able to effectively accommodate the effects of system uncertainties. The paper proposes an MPPT scheme for a WECS with a PMSG. The major advantage of using a PMSG is its ability to handle a wide range of rotor speeds which correspond to a large range of wind speeds. In a PMSG, the frequency and amplitude of the output voltage vary with wind speed. In order to maintain a narrow range of dc link voltage, the proposed wind generation system uses a dc-dc converter with buckboost feature which can step up or step down the rectified voltage by controlling its duty cycle. Also, in the PWM inverter, another closed-loop is designed to accurately track the maximum power point by shifting the phase angle of the output voltage with respect to that of the grid voltage. II. DESCRIPTION OF THE WECS SET UP The functional block diagram of the proposed wind energy MPPT system is shown in Fig. 1. The wind speed measured using an anemometer is utilized to compute the maximum * Pmax Pout _ Power Calculator Igrid PI PWM Modulator Buck-Boost Converter Wind Speed Vw Wind Turbine Tm PMSG Three-phase Diode Rectifier Vrec Vdc Grid Vgrid Three-phase PWM Inverter ωm Duty Cycle Gate Pulse Generator PI _ Vdcref Fig. 1. Block diagram of proposed MPPT system power Pmax* which is used as the reference for the outer power control loop. While extracting maximum power, the wind turbine runs the PMSG at the optimum speed ωm. The threephase variable frequency output voltage from the PMSG is rectified using a three-phase diode rectifier and fed as the input to the buck-boost dc to dc converter. At any wind speed, the output voltage of the buck-boost converter Vdc can be regulated at a constant level by controlling the duty cycle of the active switch through a PI controller as shown in Fig. 1. The reference voltage Vdcref is chosen to match of the output of the PWM inverter which will be the grid voltage. The use of a buck-boost converter allows the WECS to operate over a wide range of wind speeds (very low to very high) but within the permissible limits. The output of the buck-boost converter is fed to the PWM inverter whose reference sine input is taken from the grid. Keeping the modulation index constant, the phase of the inverter output voltage can be shifted using a feedback loop. This done by comparing the reference power Pmax* and the real power that is fed to the grid. A second PI controller modifies the angle between the grid voltage and corresponding current in the same phase. By varying the phase angle, the proposed system can extract maximum power from the wind turbine and supply the grid. ⎛C ⎞ C p ( λ , β ) = C1 ⎜ 2 − C3 β − C4 ⎟ e ⎝ λi ⎠ − C5 λi + C6 λ (2) with 1 λi = 1 0.035 − 3 λ + 0.08β β + 1 (3) where β is blade pitch angle, and λ is defined by λ= ωm R Vw . (4) In (4), ωm is the turbine angular velocity and R is the turbine radius. In small wind turbine generation systems, β is rarely changed. III. MATHEMATICAL MODEL A. Wind Turbine The mechanical power output from the wind turbine is given by [1] 1 Pm = ρ AC pVw3 (1) 2 where ρ is the air density, A is the sweep area of the turbine blades, Vw is wind speed, Cp is the aerodynamic power coefficient which is a function of the pitch angle β and the tip speed ratio λ . Since ρ and A are constant parameters, the wind turbine can produce maximum power under a certain wind speed only when the turbine operates at the maximum Cp. A generic equation is used to express Cp. This equation, based on the turbine characteristics of [11], is given by Fig. 2. C p − λ curve of the wind turbine Fig. 2 shows the C p − λ curve described by (2) for the wind turbine considered in this paper. From Fig. 2 and the definition of λ , at a specific wind speed, there is a unique wind turbine shaft speed to achieve the maximum power coefficient C p max . When C p is controlled to be at its maximum value, the maximum mechanical power is extracted from the wind energy for any wind speed. B. PMSG The steady-state-induced voltage and torque equations of a PMSG are given by 3 Te = K t I (5) E = K e ωm (6) The mechanical characteristics of the PMSG can be described by d 1 ωm = (Tm − Te − F ωm ) (7) dt J where J is combined inertia of the rotor and load, Tm is the mechanical torque input from the wind turbine, Te is electromagnetic torque, and F is the combined viscous friction of the rotor and load. In the simulation, an alternate model for the PMSG is used. For this, the output voltage of the PMSG at any given speed and output current is obtained from the experimental characteristics. Fig. 3 shows the illustrative characteristics of the phase voltage as a function of load current at different speeds. The drop in the speed with load current represents the internal drop of the PMSG which is partly due to the winding impedance. The per-phase output voltage is given by Fig. 3. Illustrative characteristics of the phase voltage as a function of load current at different speeds Vm = K1ωr - K 2 I m (8) where K1 is a constant for the PMSG calculated from the experimental characteristics, K2 is the equivalent impedance constant, and Im is the amplitude of the sinusoidal current drawn from the PMSG. The rms value of the line-line voltage from the PMSG is given by Vllrms = 3 2 Vm . D. Buck-boost Converter Fig. 4. Power circuit of Buck-boost converter The rectified voltage Vrec is stepped up/down by the buckboost converter (Fig. 4) whose output voltage Vdc and output current Idc are given respectively by Vdc = − I dc = D Vrec 1− D 1− D I rec D (11) (12) where D is the duty cycle. The inductor is designed to have continuous current. From the above expression, it can be seen that the polarity of the output voltage is always negative as the duty cycle goes from 0 to 1. Apart from the polarity, this converter is capable operating either the step-up mode (as a boost converter) or step-down mode (as a buck converter). In order to obtain a constant dc output voltage, the difference between the desired output voltage and the actual output voltage is used to vary the duty cycle of the buck-boost converter under different wind speeds. It is worth noting that buck-boost converter maintains a constant power like other dc to dc converter, when the losses are neglected. E. PWM Phase shift Control The buck-boost converter along with the voltage control loop supplies a constant dc voltage to the three-phase PWM inverter as shown in Fig. 5. (9) C. Diode rectifier The output from the PMSG is rectified using a three-phase rectifier whose output voltage Vrec is given by [12]. Vrec = 3 2 π Vllrms (10) If ignore the losses of diodes, diode rectifier does not change the power. It only uses to convert ac to dc. Fig. 5. Block diagram of PWM phase-shift controller The PWM inverter converts a dc voltage into a three-phase ac voltage which is applied to the grid through smoothing inductors including their parasitic resistors. The currents flowing into the grid along with the inverter output voltages are measured for actual power calculation. In order to have a phase-shift angle with respect to the grid voltage, another PI controller is utilized. The PWM circuit compares the phaseshifted reference sine wave (obtained from both the grid and 4 the PI controller) and a high-frequency triangular wave with a large frequency modulation index mf = ft/f and a nominal amplitude modulation index ma = Vgird/Vt where ft and Vt are the frequency and amplitude of the triangular wave respectively, and f (60Hz) and Vgrid are the frequency and amplitude of the phase-shifted reference sine wave from the grid. The PWM inverter provides a three-phase output with voltage vinv and current iinv . The relation between vinv and vdc is given by [12] Vinvllrms = 0.612maVdc (13) where Vinvllrms is the rms value of the line-to-line voltage. If both the three-phase PMSG and three-phase grid operate under balanced steady-state conditions, and the instantaneous grid terminal voltage in phase A is vgridan = V ∠δ (line-toneutral voltage), the equation for vinvan will be vinvan = V ′∠ (δ + α ) (14) where V ′ is the amplitude of inverter output voltage and α is the phase shift angle provided by the PI controller. According to equation (9), if ma is fixed and Vdc is maintained constant, V ′ will also be constant. If the per-phase impedance of the line filter is Z ∠θ , the current fed to the grid by phase A can be expressed as vinvan − vgridan V ′∠ (δ + α ) − V ∠δ igrida = = = I ∠β . (15) Z ∠θ Z ∠θ Under balanced operating conditions, the total power to the grid P3φ is given by [13] P3φ = p3φ ( t ) = vgridan igrida + vgridbn igridb + vgridcn igridc = 3VI cos (δ − β ) (16) where p3φ ( t ) is the instantaneous power delivered by all three phases. Equation (16) shows that the average power is equal to the total instantaneous power delivered to the grid which can be easily calculated using measured three-phase currents and voltages. In addition, equation (16) shows that the actual power is not a function of time, but depends on vectors vgridln and igrid . The phase-shift control strategy varies the phase angle of the inverter output voltage while keeping its amplitude constant at V ′ (the amplitude of grid voltage). The line impedance in each phase is a constant as well. Besides, δ is the phase angle of grid which cannot be varied. From (14), (15), and (16), it is seen that P3φ can be varied by varying the phase-shift angle α . IV. MPPT PRINCIPLE Optimal operation of the PMSG-based WECS is to extract the maximum power from wind. According to (1), the maximum power at a given wind speed can be extracted when Cp, which is a function of the pitch angle β and the tip speed ratio λ , is maximum. Since β is fixed, λ has to be at its optimal value. From equation (4), it is seen that λ can be regulated by changing the turbine angular velocity ωm . Thus, the optimal control of the WECS means that the system has to operate at the optimal value of the rotating speed of the PMSG at different wind speeds. Fig. 6. Mechanical power versus rotating speed for different wind speeds Fig. 6 represents the relation between generator speed and output power for different wind speeds. It is seen that the maximum power output occurs at different rotating speeds for different wind speeds. The role of the MPPT control strategy is to track the maximum power curve shown in Fig. 6. Fig. 7. Vector representations of inverter output current and voltage without and with phase-shift control The vector representation of equation (15) is shown in Fig. 7. Fig. 7(a) shows the case without phase-shift control while Fig. 7(b) shows the case with phase-shift control. It is obvious that the value of V − V ′ in Fig. 7(a) is smaller than that in Fig. 7(b). Since Z is a constant parameter of the circuit, the output current in the system without phase-shift control is smaller than that of a system with phase-shift control. Initially, if the system operates at a higher value of ωm, then Pm* will be higher than the actual power which increases the phase shift. As a result, the output current will increase. When the output current increases, the input current of the inverter should also increase because of conservation of energy (neglecting the losses in the inverter). From equation (12), the output current of the diode rectifier also increases, which leads to an increase in the PMSG current. Since the PMSG current is proportional to electromagnetic torque Te, Te is raised as well. Then the d ωm decreases as in equation (7), which means the value of dt PMSG decelerates and settles down at the optimum ωm which is lower than the initial speed. V. SIMULATION RESULTS The model of the PMSG-based variable-speed wind turbine system in Fig. 1 is built mainly using Matlab/Simulink dynamic system simulation software for simulating the 5 behavior of the entire system subjected to wind speed variations. The simulation model is developed for a 500W industrial permanent magnet synchronous alternator. The parameters of the turbine and the PMSG used are given in Table I. The power converters and both the duty cycle and phase-shift control algorithms are also implemented in the model. The sampling time used for the simulation is 10μs. The wind speed waveform is simulated by TurbSim software based on the data for the state of North Dakota in US published by the Department of Energy's Wind Program and the National Renewable Energy Laboratory (NREL) [14]. TABLE I PARAMETER OF THE TURBINE-GENERATOR SYSTEM WIND TURBINE Air Density ( ρ ) Radius of the Turbine Blades ( r ) PMSG Rated Voltage, phase Rated Output Rated Speed Rated Frequency Stator Phase Resistance ( Rs) Inductances ( Ld=Lq ) Inertia ( J ) Friction Factor ( F ) Pole Pairs K1 ( in equation 6 ) K2 ( in equation 6 ) BUCK-BOOST CONVERTER L C PWM MODULATOR Amplitude Modulation Index Frequency of Triangular Wave 1.25 0.525 kg/m3 m 115 500 3428 400 1.57 3.51 0.0008 0.00005 7 0.0353 1.939 V VA rpm Hz Ω mH kg.m2 N.m.s 5 220 mH μF 0.8 1200 Hz Fig. 8. Plot of stepped wind speed profile, maximum power Pmax* and output power P V/(rad/s) Ω The operation of the MPPT scheme for a wind speed profile with step changes is shown in Fig. 8 where the wind speed and output power are plotted. Fig. 9 shows the variation of rotating speed and the phase-shift angle which is controlled as expected. The sight overshoot in the response of the PMSG’s rotating speed ωm shows that the controller parameters are set properly. From both these responses, it is seen that the phaseshift control system can extract the maximum power from wind even when the wind speed changes sharply. Instead of a stepped wind speed, a variable wind speed is given as a practical one. In order to ensure supplying a constant input voltage (higher than grid voltage) to the phaseshift closed-loop, duty cycle is regulated in buck-boost converter. Fig. 9. Waveforms of rotating speed of PMSG and phase shift angle Instead of the stepped wind-speed profile, the system is tested with a practical profile. Fig. 10 shows the plot of the wind speed profile which is simulated by TurbSim software for the wind speed levels in North Dakota state, the corresponding maximum power Pmax* calculated from the wind speed, and the actual power P fed to the grid. It is seen that the actual power tracks the maximum power very well in the higher wind speed range. However, some sharp variations are not tracked quite well. That is because of the delay in the phase-shift controller which is found to be somewhat higher when achieving robustness. The whole system could be unstable when there are sharp transitions in the wind speed. The balancing of the rotating speed and the torque in the PMSG is the key point in MPPT. The torque is varied following the changes in the wind speed. The phase-shift control strategy implements the regulation of the rotating speed ωm in PMSG by shifting the phase angle which is shown in Fig. 11. The duty cycle of the buck-boost converter is controlled to give a constant dc link voltage to the grid. In Fig. 12, the variation of duty cycle for the wind speed profile of Fig. 10 is shown and it stays around 0.57. As a result, the output voltage is kept constant at 250V as shown in Fig. 12. 6 Fig. 10. Plot of wind speed profile (Turbsim), maximum power Pmax* and output power P Fig. 13. Waveforms of output current (igrid) and the zoom-in plot Fig. 14. Waveforms of inverter line-line output voltage and grid voltage Fig. 11. Waveforms of rotating speed of PMSG and phase shift angle VI. CONCLUSIONS Fig. 12. Waveforms of duty cycle and output voltage of buck-boost converter Figure 13 shows the sinusoidal waveform of output current igrid. Since the grid voltage is supposed to be independent of PMSG output, changing the output current means that the output power is varied under different wind speeds to match the maximum power. The oscillations in current waveform are the high frequency ripple at the triangle wave frequency (1200 Hz). This effect can be further reduced using a low-pass filter. Figure 14 shows the inverter line-line voltage and the corresponding grid voltage. The inverter output voltage contains discrete pulses caused by the inverter switches and it is clear seen that there is a phase shift between the two. This paper proposes and demonstrates an MPPT strategy for a PMSG-based variable-speed wind turbine generator system. In this strategy, the dc voltage is controlled at a constant value and applied as the input voltage to the inverter by a buck-boost converter under variable wind speeds. Then the phase angle of the ac output voltage is shifted by PWM inverter in order to extract the maximum power from the wind for a wide range wind speeds. The PMSG is simulated using an approximate model derived from the experimental load characteristics. The feedback control scheme uses a power control loop and feeds power to the grid. The simulation results show that the output power follows the reference wind speed and the computed maximum power. The output current has an acceptable sinusoidal waveform. VII. REFERENCES [1] [2] [3] M. Chinchilla, S. Amaltes, and J.C. Burgos, “Control of permanentmagnet generators applied to variable-speed wind-energy systems connected to the grid”, IEEE Trans. Energy Conversion, Vol. 21, No. 1, pp. 130 – 35, March 2006. D. Svechkarenko, “Simulations and control of direct driven permanent magnet synchronous generator”, Project Report, Department of Electrical Engineering, Royal Institute of Technology, Sweden, Dec. 2005. K. Tan and S. 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Razhid, Power Electronics: Circuits Devices and Applications, 3rd Ed., Prentice Hall, 2003. J. D. Glover, M. S. Sarma, Power System Analysis and Design, 3rd ed., Thomson, p. 58. "North Dakota 50-meter wind resource map," published by The Department of Energy's Wind Program and the National Renewable Energy Laboratory (NREL), Available: http://www.windpoweringamerica.gov/maps_template.asp?stateab=nd VIII. BIOGRAPHIES Xin Wang received the B.E. degree from the College of Automation Engineering, Nanjing University of Aeronautics and Astronautics. She is currently pursuing the Master degree in Electrical and Computer Engineering at North Dakota State University, Fargo. Subbaraya Yuvarajan (SM’84) received his B.E. (Hons) degree from University of Madras, India in 1966 and M.Tech. degree from Indian Institute of Technology, Chennai, India in 1969. He received his Ph.D. degree from Indian Institute of Technology, Chennai, India in 1981. Dr. Yuvarajan has worked at Indian Institute of Technology, Chennai before coming to USA in 1983. He has been a professor of Electrical and Computer Engineering, North Dakota State University, Fargo since 1995. His areas of interest are Electronic Circuits, Power Electronics, and Power Conversion for Renewable Energy Sources. Lingling Fan (SM’08) is an assistant professor in the Electrical Engineering Department, University of South Florida, Tampa, FL. She received her B.S. and M.S. degrees in Electrical Engineering from Southeast University, Nanjing, China in 1994 and 1997 respectively. She received her Ph.D. degree from West Virginia University in 2001. Before joining University of South Florida, Dr. Fan has worked for Midwest ISO, St. Paul, Minnesota and North Dakota State University, Fargo. Her research interests include the control of renewable energy sources, protection of power systems, and power system stability and economics.
